Cholesky Decomposition Techniques in Electronic Structure Theory

Aquilante, Francesco; Boman, Linus; Boström, Jonas; Koch, H.; Lindh, Roland; Merás, Alfredo Sánchez de; Pedersen, Thomas Bondo

doi:10.1007/978-90-481-2853-2_13

Cited by 102 publications

(119 citation statements)

References 93 publications

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“…It has been employed in the iterative updates of plane-wave DFT calculations, 60 where the full Fock matrix is enormous and thus, evaluating a narrow rectangular matrix is far preferable to an enormous square matrix. Indeed, the idea of constructing this economized version of K was mentioned briefly by Aquilante et al, 61 but we have found no prior or subsequent discussion in the literature. The important point that has not yet been accomplished is to demonstrate how formation of an economized K matrix can be used for computational advantage with AO basis sets.…”

Section: A Economization Of the K Matrixmentioning

confidence: 90%

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Manzer

Horn

Mardirossian

et al. 2015

The Journal of Chemical Physics

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Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C 68 H 22 hydrogen-terminated graphene fragment, our algorithm yields a 14× speedup over the conventional algorithm and a speedup of 3.3× over RI-K. C 2015 AIP Publishing LLC. [http://dx

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Section: A Economization Of the K Matrixmentioning

confidence: 90%

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Manzer

Horn

Mardirossian

et al. 2015

The Journal of Chemical Physics

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“…48,49 The cc-pVTZ basis set was used in all FDET calculations except for the bromine model system, where the aug-cc-pVDZ basis set was applied. 50,51 The implementation uses Cholesky-based ab initio density fitting 52 to approximate the two-electron integrals: the required auxiliary basis set is not pre-optimized through data-fitting but it is generated through Cholesky decomposition of each atomic sub-block of the integral matrix. Next to the computational advantage compared to conventional integral calculations, this type of density fitting guarantees to a large extent complete error control in the computed energy 53,54 and energy gradients.…”

Section: Numerical Detailsmentioning

confidence: 99%

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

Zech

Aquilante

Wesołowski

2015

The Journal of Chemical Physics

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Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles -embedded wave functions are only auxiliary objects used to obtain stationary densities -working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities. C 2015 AIP Publishing LLC. [http://dx

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“…[187] Calibration of the resulting ABS on small to medium sized complexes with a variety of oxidation states indicates that negligible fitting errors are produced. [185,187,[190][191][192] An alternative to DF using preoptimized ABSs are methods based on Cholesky decomposition (CD) techniques, and although such methods have been the subject of recent reviews, [194,195] they are briefly recapped below. A symmetric positive definite matrix V can be decomposed into the product of a lower triangular matrix, L, and its adjoint:…”

Section: Auxiliary Basis Setsmentioning

confidence: 99%

Gaussian basis sets for molecular applications

Hill¹

2012

Int J of Quantum Chemistry

188

155

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The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom-centered, energy-optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design.

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Cholesky Decomposition Techniques in Electronic Structure Theory

Cited by 102 publications

References 93 publications

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

Gaussian basis sets for molecular applications

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